Question

use the graph of two triangles for items 1 and 2. select all the true statements given that ( \triangle pqrcong\triangle stu ). a ( pq = st ) b ( pq = tu ) c ( mangle r=mangle u ) d ( mangle p=mangle u ) e ( qr = su ) f ( mangle q=mangle t )

Explanation:

Step1: Recall the properties of congruent triangles

When \(\triangle PQR\cong\triangle STU\), corresponding sides and corresponding angles are equal. That is \(PQ = ST\), \(QR=SU\), \(PR = TU\), \(\angle P=\angle S\), \(\angle Q=\angle T\), \(\angle R=\angle U\)

Step2: Check each option

• Option A:

Since \(\triangle PQR\cong\triangle STU\), by the property of congruent triangles, \(PQ\) and \(ST\) are corresponding sides. So \(PQ = ST\). This option is correct.

• Option B:

\(PQ\) and \(TU\) are not corresponding sides. \(PQ = ST\) and \(PR=TU\) (from congruent - triangle side - correspondence). So \(PQ
eq TU\). This option is incorrect.

• Option C:

\(\angle R\) and \(\angle U\) are corresponding angles. By the property of congruent triangles \(\angle R=\angle U\), so \(m\angle R = m\angle U\). This option is correct.

• Option D:

\(\angle P\) and \(\angle S\) are corresponding angles (\(\angle P=\angle S\)), \(\angle U\) and \(\angle R\) are corresponding angles. So \(m\angle P
eq m\angle U\). This option is incorrect.

• Option E:

\(QR\) and \(SU\) are corresponding sides. By the property of congruent triangles \(QR = SU\). This option is correct.

• Option F:

\(\angle Q\) and \(\angle T\) are corresponding angles. By the property of congruent triangles \(\angle Q=\angle T\), so \(m\angle Q = m\angle T\). This option is correct.

Answer:

A. \(PQ = ST\), C. \(m\angle R=m\angle U\), E. \(QR = SU\), F. \(m\angle Q=m\angle T\)